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Root of a complex number

The root of a complex number must be reduced to an arithmetic root in order to calculate it, with

 


Explanation

Complex numbers can be converted by using the definition of the imaginary unit i 2 = – 1. You then no longer have a minus sign. With a multiplication you get

where a and b are positive numbers.

 


Example 1

The result of the calculation

yields a negative number, and I'm sure you didn't expect that to happen. So it's not

          

 


Example 2

The calculation

          

is wrong. The feature

applies only to arithmetic roots. Algebraic roots must first be reduced to arithmetic roots.

 


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